Question 319: Electromagnetic Induction

Question

the magnetic flux (in weber) in a closed circuit of resistance $$20 \Omega$$ varies with time $$t$$ second according to equation $$\phi=5 t^2-6 t+9$$. The magnitude of induced current at $$t=0.2$$ second is

Accepted Answer

To find the magnitude of the induced current in the circuit at $$t = 0.2$$ second, we will use Faraday's law of electromagnetic induction. According to Faraday's law, the induced electromotive force (EMF) in a circuit is equal to the negative rate of change of magnetic flux through the circuit. Mathematically, this is expressed as:
$$ EMF = -\frac{d\phi}{dt} $$
Given that the magnetic flux, $$\phi=5t^2-6t+9$$, we first need to find its derivative with respect to time $$(t)$$ to get the EMF:
$$ \frac{d\phi}{dt} = \frac{d}{dt}(5t^2-6t+9) = 10t - 6 $$
Now, substituting $$t = 0.2$$ seconds into the derivative, we get the EMF at $$t = 0.2$$:
$$ EMF = 10(0.2) - 6 = 2 - 6 = -4 \, 	ext{V} $$
The magnitude of EMF is 4 V (we consider magnitude so we'll not worry about the negative sign which indicates direction).
Using Ohm's Law, we find the induced current, $$I$$, in a circuit with the resistance $$R$$, as:
$$ I = \frac{EMF}{R} $$
Given that the resistance $$R = 20 \, \Omega$$, we substitute the EMF value to find the induced current:
$$ I = \frac{4}{20} = 0.2 \, 	ext{A} $$
Therefore, the magnitude of the induced current at $$t = 0.2$$ second is
0.2 A
, which corresponds to
Option C
.

Answer

0.8 A

Answer

1 A

Answer

0.2 A

Answer

0.4 A

Electromagnetic Induction

the magnetic flux (in weber) in a closed circuit of resistance $20 \Omega varies with time t second according to equation \phi=5 t^2-6 t+9. The magnitude of induced current at t=0.2$ second is

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